It is given that and BC QR =2 3 then ar( ) ar( ) =? - Vidyadip

MCQ

It is given that $\triangle\text{ABC}\sim\triangle\text{PQR}$ and $\frac{\text{BC}}{\text{QR}}=\frac{2}{3}$ then $\frac{\text{ar}(\triangle\text{PQR})}{\text{ar}(\triangle\text{ABC})}=?$

A
$\frac{2}{3}$
B
$\frac{3}{2}$
C
$\frac{4}{9}$
✓
$\frac{9}{4}$

✓

Answer

Correct option: D.

$\frac{9}{4}$

$\triangle\text{ABC}\sim\triangle\text{PQR}$ and $\frac{\text{BC}}{\text{QR}}=\frac{2}{3}$
$\Rightarrow\frac{\text{QR}}{\text{BC}}=\frac{3}{2}$
$\frac{\text{ar}(\triangle\text{PQR})}{\text{ar}(\triangle\text{ABC})}=\frac{\text{QR}^2}{\text{BC}^2}=\frac{3^2}{2^2}=\frac{9}{4}$
So, the ratio is $9 : 4.$

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